Author: Tsutomu Sasao Publisher: Springer Science & Business Media ISBN: 1461313856 Category : Technology & Engineering Languages : en Pages : 344
Book Description
Representations of Discrete Functions is an edited volume containing 13 chapter contributions from leading researchers with a focus on the latest research results. The first three chapters are introductions and contain many illustrations to clarify concepts presented in the text. It is recommended that these chapters are read first. The book then deals with the following topics: binary decision diagrams (BDDs), multi-terminal binary decision diagrams (MTBDDs), edge-valued binary decision diagrams (EVBDDs), functional decision diagrams (FDDs), Kronecker decision diagrams (KDDs), binary moment diagrams (BMDs), spectral transform decision diagrams (STDDs), ternary decision diagrams (TDDs), spectral transformation of logic functions, other transformations oflogic functions, EXOR-based two-level expressions, FPRM minimization with TDDs and MTBDDs, complexity theories on FDDs, multi-level logic synthesis, and complexity of three-level logic networks. Representations of Discrete Functions is designed for CAD researchers and engineers and will also be of interest to computer scientists who are interested in combinatorial problems. Exercises prepared by the editors help make this book useful as a graduate level textbook.
Author: Publisher: ISBN: Category : Languages : en Pages :
Book Description
All discrete function representations become exponential in size in the worst case. Binary decision diagrams have become a common method of representing discrete functions in computer-aided design applications. For many functions, binary decision diagrams do provide compact representations. This work presents a way to represent large decision diagrams as multiple smaller partial binary decision diagrams. In the Boolean domain, each truth table entry consisting of a Boolean value only provides local information about a function at that point in the Boolean space. Partial binary decision diagrams thus result in the loss of information for a portion of the Boolean space. If the function were represented in the spectral domain however, each integer-valued coefficient would contain some global information about the function. This work also explores spectral representations of discrete functions, including the implementation of a method for transforming circuits from netlist representations directly into spectral decision diagrams.
Author: Whitney Jeanne Townsend Publisher: ISBN: Category : Decision logic tables Languages : en Pages :
Book Description
All discrete function representations become exponential in size in the worst case. Binary decision diagrams have become a common method of representing discrete functions in computer-aided design applications. For many functions, binary decision diagrams do provide compact representations. This work presents a way to represent large decision diagrams as multiple smaller partial binary decision diagrams. In the Boolean domain, each truth table entry consisting of a Boolean value only provides local information about a function at that point in the Boolean space. Partial binary decision diagrams thus result in the loss of information for a portion of the Boolean space. If the function were represented in the spectral domain however, each integer-valued coefficient would contain some global information about the function. This work also explores spectral representations of discrete functions, including the implementation of a method for transforming circuits from netlist representations directly into spectral decision diagrams.
Author: R. C. Gonzalez Publisher: ISBN: Category : Languages : en Pages : 133
Book Description
As applications of digital systems continue to expand, the need arises for better methods of analysis of functions of discrete variables. Particularly important is the ability to gauge accurately the difficulty of a problem; this leads to measuring a function's complexity. This in turn requires an implementation-independent model of function evaluation, one that also shows the contribution of individual variables to the function's complexity. One such model, called a decision tree, is introduced; it is essentially a sequential evaluation procedure where, at each step, a variable's value is determined and the next action chosen accordingly. Decision trees have been used in switching circuits, data bases, pattern recognition, machine diagnosis, and remote data processing. The activity of a variable, a new concept that measures the contribution of a variable to the complexity of a function, is defined and its relation to decision trees is described. Based upon these results (which can be generalized to recursive functions and hierarchies of relations), a complexity measure is proposed. The use of that measure and of the concept of activity in testing large systems (where a number of variables may be inaccessible) is then examined, with particular emphasis on continuous checking of systems in operation. (Author).
Author: N.Ja. Vilenkin Publisher: Springer Science & Business Media ISBN: 940113538X Category : Mathematics Languages : en Pages : 635
Book Description
This is the first of three major volumes which present a comprehensive treatment of the theory of the main classes of special functions from the point of view of the theory of group representations. This volume deals with the properties of classical orthogonal polynomials and special functions which are related to representations of groups of matrices of second order and of groups of triangular matrices of third order. This material forms the basis of many results concerning classical special functions such as Bessel, MacDonald, Hankel, Whittaker, hypergeometric, and confluent hypergeometric functions, and different classes of orthogonal polynomials, including those having a discrete variable. Many new results are given. The volume is self-contained, since an introductory section presents basic required material from algebra, topology, functional analysis and group theory. For research mathematicians, physicists and engineers.
Author: Vlad P. Shmerko Publisher: CRC Press ISBN: 1420066218 Category : Technology & Engineering Languages : en Pages : 841
Book Description
Emphasizes the Basic Principles of Computational Arithmetic and Computational Structure Design Taking an interdisciplinary approach to the nanoscale generation of computer devices and systems, Computer Arithmetics for Nanoelectronics develops a consensus between computational properties provided by data structures and phenomenological properties of nano and molecular technology. Covers All Stages of the Design Cycle, from Task Formulation to Molecular-Based Implementation The book introduces the theoretical base and properties of various data structures, along with techniques for their manipulation, optimization, and implementation. It also assigns the computational properties of logic design data structures to 3D structures, furnishes information-theoretical measures and design aspects, and discusses the testability problem. The last chapter presents a nanoscale prospect for natural computing based on assorted computing paradigms from nature. Balanced Coverage of State-of-the-Art Concepts, Techniques, and Practices Up-to-date, comprehensive, and pragmatic in its approach, this text provides a unified overview of the relationship between the fundamentals of digital system design, computer architectures, and micro- and nanoelectronics.
Author: Horand Störmer Publisher: Springer Science & Business Media ISBN: 3642615198 Category : Business & Economics Languages : en Pages : 160
Book Description
In this book binary functions and their representation by implicants or implicates are described. In particular minimal representations by prime implicants or prime implicates are given. Such representations generalize the minimal representations of the usual Boolean functions. It is shown that implicants (implicates) of discrete functions may be constructed with the help of implicants (implicates) of binary functions. One substantial application is the description of the reliability structure of technical systems, another is the use of binary respectively discrete functions to classify objects which are described by the grades of certain attributes. Finally a class of Boolean algebras of practical importance (set algebras, indicator algebras, algebras of classes of propositions) are considered. The elements of such algebras have representations which are strongly connected with the representations of binary functions.
Author: Tsutomu Sasao
Author: 
Author: Whitney Jeanne Townsend
Author: Ivo Ĭordanov Dami︠a︡nov
Author: Bernard M. E. Moret
Author: Cheng Fu
Author: R. C. Gonzalez
Author: N.Ja. Vilenkin
Author: Vlad P. Shmerko
Author: Horand Störmer